On A Class Of Dirichlet Problem With Discontinuous Nonlinearities Which Super-linear Or Asymptotically Linear At Infinity

The main purpose of the paper is to study the existence of a positive solution for a Class of Dirichlet problem with discontinuous nonlinearities:and some new existence theorems are obtained, where Ω, (?) R~N is a bounded domain with smooth boundary, f : (Ω|-) × R→ R is locally bounded and is super-linear or asymptotically linear at infinity. Our results improve and develop previous some corresponding results.